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Journal of Marine Science and Technology

, Volume 16, Issue 4, pp 448–461 | Cite as

Broaching prediction of a wave-piercing tumblehome vessel with twin screws and twin rudders

  • Hirotada HashimotoEmail author
  • Naoya Umeda
  • Akihiko Matsuda
Original Article

Abstract

The new intact stability criteria which are under development at the International Maritime Organization (IMO) are required to cover a broaching phenomenon, well known as a great threat to high-speed vessels which can lead to capsizing. Some reports exist which demonstrate that their numerical models can predict a highly nonlinear phenomenon of broaching. However, additional validation studies are needed for unconventional vessels, in addition to conventional ones, to develop direct stability assessment methods for the new intact stability criteria. In this research, we selected as the subject ship a wave-piercing tumblehome vessel with twin screws and twin rudders, a design expected to be one of a new generation of high-speed monohull ships. Firstly, a series of captive model tests were conducted to measure the resistance, the manoeuvring forces, the wave-exciting forces, the heel-induced hydrodynamic forces, and the roll restoring variation for the unconventional tumblehome vessel. Secondly, the existing mathematical model which had been developed for broaching prediction of conventional vessels with a single propeller and a single rudder was extended to unconventional vessels with twin propellers and twin rudders. Finally, comparisons between numerical simulations and the existing free running model experiments were conducted. As a result, it was demonstrated that fair quantitative prediction of broaching is realised when the rudder force variation, the roll restoring variation and the heel-induced hydrodynamic force for large heel angles are taken into account.

Keywords

Broaching Wave-piercing tumblehome vessel Following and stern quartering waves Mathematical model Twin screws Twin rudders Superstructure 

List of symbols

aH

Interaction factor between hull and rudder

ARP

Area of port-side rudder

ARS

Area of starboard-side rudder

B(x)

Breadth of each section

c

Wave celerity

CT

Total resistance coefficient

d(x)

Draught of each section

Dp

Propeller diameter

Fn

Nominal Froude number

g

Gravitational acceleration

GZ

Righting arm

GZW

Wave effect on righting arm

H

Wave height

Ixx

Moment of inertia in roll

Izz

Moment of inertia in yaw

Jxx

Added moment of inertia in roll

Jzz

Added moment of inertia in yaw

k

Wave number

Kp

Derivative of roll moment with respect to roll rate

Kr

Derivative of roll moment with respect to yaw rate

KR

Rudder gain

KT

Thrust coefficient of propeller

Kv

Derivative of roll moment with respect to sway velocity

KW

Wave-induced roll moment

Kδ

Derivative of roll moment with respect to rudder angle

\( K_{{{\updelta}}}^{\text{W}} \)

Derivative of wave effect on roll moment with respect to rudder angle

Kϕ

Heel-induced hydrodynamic force in roll

lR

Correction factor for flow-straightening effect due to yaw rate

m

Ship mass

mx

Added mass in surge

my

Added mass in sway

n

Propeller revolution number

NH

Yaw hull force

Nr

Derivative of yaw moment with respect to yaw rate

NT

Yaw moment produced by the difference of the thrust of two propellers

Nv

Derivative of yaw moment with respect to sway velocity

NW

Wave-induced yaw moment

Nδ

Derivative of yaw moment with respect to rudder angle

\( N_{{{\updelta}}}^{\text{W}} \)

Derivative of wave effect on yaw moment with respect to rudder angle

Nϕ

Heel-induced hydrodynamic force in yaw

p

Roll rate

r

Yaw rate

R

Ship resistance

S(x)

Area of each section

Sy(x)

Added mass of each section in sway

Syln(x)

Added moment of inertia of each section in roll

t

Time

tp

Thrust deduction factor

T

Propeller thrust

TD

Time constant for differential control

TE

Time constant for steering gear

u

Surge velocity

uPPW

Wave particle velocity at port-side propeller

uPSW

Wave particle velocity at starboard-side propeller

uRPW

Wave particle velocity at port-side rudder

uRSW

Wave particle velocity at starboard-side rudder

U

Ship speed

ν

Sway velocity

vRPW

Wave particle velocity at port-side rudder

vRSW

Wave particle velocity at starboard-side rudder

wp

Effective propeller wake fraction

xH

Longitudinal position of centre of interaction force between hull and rudder

xR

Longitudinal position of rudder

xP

Longitudinal position of propeller

XW

Wave-induced surge force

Xϕ

Heel-induced hydrodynamic force in surge

YH

Sway hull force

yPP

Horizontal position of port-side propeller

yPS

Horizontal position of starboard-side propeller

Yr

Derivative of sway force with respect to yaw rate

Yv

Derivative of sway force with respect to sway velocity

YW

Wave-induced sway force

Yδ

Derivative of sway force with respect to rudder angle

YδW

Derivative of wave effect on sway force with respect to rudder angle

Yϕ

Heel-induced hydrodynamic force in sway

zH

Vertical position of centre of sway force due to lateral motions

zHR

Vertical position of centre of effective rudder force

zP

Vertical position of propeller

Λ

Rudder aspect ratio

χ

Heading angle from wave direction

χc

Desired heading angle for auto pilot

γR

Flow-straightening effect coefficient

δ

Rudder angle

εR

Wake ratio between propeller and hull

κp

Interaction factor between propeller and rudder

ϕ

Roll angle

λ

Wave length

ρ

Water density

τ

Trim

ω

Wave frequency

ωe

Encounter frequency

ξG

Longitudinal position of the centre of gravity from a wave trough

ζa

Wave amplitude

ζG

Sinkage

Notes

Acknowledgments

This research was supported by the US Office of Naval Research contract N00014-09-1-1089 under the administration of Dr. Patrick Purtell. It was partly supported by a Grant-in Aid for Scientific Research of the Japan Society for Promotion of Science (No.21360427).

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Copyright information

© JASNAOE 2011

Authors and Affiliations

  • Hirotada Hashimoto
    • 1
    Email author
  • Naoya Umeda
    • 1
  • Akihiko Matsuda
    • 2
  1. 1.Graduate School of EngineeringOsaka UniversitySuitaJapan
  2. 2.National Research Institute of Fisheries EngineeringKamisuJapan

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